The news was confirmed via a tweet from the Tigers this afternoon, which revealed that the midfielder had joined for "an undisclosed fee".
"We are delighted to confirm Robert Snodgrass as our second major signing of the summer. Snodgrass arrives from @NorwichCityFC for an undisclosed fee, with the midfielder signing a three-year contract with the Tigers #UTT," read the tweet.
Meanwhile, Snodgrass added: "Having spoken to the owners and the manager, and seen the plans they have for this club, I was very keen to be a part of it all.
"Everything the club has done to get the deal completed has been unbelievable. This is the start of an exciting new chapter for me and for my family and I just can't wait to get started now."
The 26-year-old joined Norwich from Leeds United in 2012, but had been strongly linked with a move away from the Canaries this summer.